What do the shares get them?
It has the power of a government agency without the responsibilities. It not being part of the government is a technicality given the power and authority it has.
It is part of the government, it just isn’t officially part of the government. Or you could also say that the federal reserve program is a government program which comes to exactly the same result of it being an arm of the government. Its like if some dude out in Kansas was being given trillions of dollars to save our whole existence from demons and no one was allowed to check on whether or not he was spending the money coming up with special effects.
It is identical to having a bunch of government stooges behind closed doors spending trillions with no oversight. Same exact thing.